Topic
Nonlinear programming
About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.
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TL;DR: Difficulty connected with solving the general nonlinear programming problem is discussed; several approaches that have emerged in the evolutionary computation community are surveyed; and a set of 11 interesting test cases are provided that may serve as a handy reference for future methods.
Abstract: Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing.
In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.
1,620 citations
TL;DR: The design and implementation of a new algorithm for solving large nonlinear programming problems follows a barrier approach that employs sequential quadratic programming and trust regions to solve the subproblems occurring in the iteration.
Abstract: The design and implementation of a new algorithm for solving large nonlinear programming problems is described. It follows a barrier approach that employs sequential quadratic programming and trust regions to solve the subproblems occurring in the iteration. Both primal and primal-dual versions of the algorithm are developed, and their performance is illustrated in a set of numerical tests.
1,605 citations
01 Mar 1996
TL;DR: An algorithm for solving large nonlinear optimization problems with simple bounds is described, based on the gradient projection method and uses a limited-memory BFGS matrix to approximate the Hessian of the objective function.
Abstract: An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is based on the gradient projection method and uses a limited-memory BFGS matrix to approximate the Hessian of the objective function. We show how to take advantage of the form of the limited-memory approximation to implement the algorithm efficiently. The results of numerical tests on a set of large problems are reported.
1,581 citations
Book•
01 Jan 1987TL;DR: The optimal control problem is illustrated with examples of large, sparse nonlinear programming and a comparison of optimal control problems in the context of discrete-time programming.
Abstract: Preface 1. Introduction to nonlinear programming 2. Large, sparse nonlinear programming 3. Optimal control preliminaries 4. The optimal control problem 5. Optimal control examples Appendix A. Software Bibliography, Index.
1,541 citations
TL;DR: This paper focuses on the primal version of the new algorithm, an algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints, which applies sequential quadratic programming techniques to a sequence of barrier problems.
Abstract: An algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints is described. It applies sequential quadratic programming techniques to a sequence of barrier problems, and uses trust regions to ensure the robustness of the iteration and to allow the direct use of second order derivatives. This framework permits primal and primal-dual steps, but the paper focuses on the primal version of the new algorithm. An analysis of the convergence properties of this method is presented.
1,514 citations